Question

The nation of Maximus has a marginal propensity to consume of .90 and the government has decreased taxes by a lump-sum amount of $1 billion. Assume there is no international trade or changes to the aggregate price level. a. What is the value of the tax multiplier in Maximus? b. By how much will real GDP change after the $1 billion decrease in taxes? c. If the government wanted to accomplish the same increase in real GDP you found in part (b), but with government spending instead of taxes, would the government need more than $1 billion in spending, less than $1 billion in spending, or exactly $1 billion in spending? Explain.

Answer 1

a). Consider the close economy here the goods market equilibrium is given below.

=> Y = C + I + G, here C = a + b*(Y – T), here T=lamp sum tax, G and I are exogenously fixed.

=> Y = a + b*Y – b*T + I + G, now change in “Y”, is “dY”, so differentiating the above equation totally we have.

=> dY = b*dY – b*dT + dI + dG, here dG = dI =0.

=> dY = b*dY – b*dT, => (1 – b)*dY = (-b)*dT, => dY/dT = (-b)/(1 – b) = (-0.9)/0.1 = (-9), here b = MPC.

=> the value of the tax multiplier is “(-9)” in Maximus, here we can see that the value of the multiplier is negative, => as “T” increases, => dT > 0, => “Y” will decrease, => dY < 0.

b). Now, let’s assume that “T” decreases by “1 billion”, => dT = (-1). So, from the multiplier we have, => dY = (-9)*dT = 9. So, we can say that as “T” falls by “1 billion”, => “Y” will increase by “9 billion”.

c). Now, suppose that if govt. want the same increase in “Y” but not through “T” rather through “G”, so here we need to calculate the “govt. spending” multiplier.

=> Y = C + I + G, here C = a + b*(Y – T), here T=lamp sum tax, G and I are exogenously fixed.

=> Y = a + b*Y – b*T + I + G, now change in “Y”, is “dY”, so differentiating the above equation totally we have.

=> dY = b*dY – b*dT + dI + dG, here dT = dI =0. => dY = b*dY + dG, => (1 – b)*dY = dG, => dY/dG = 1/(1 – b).

=> the govt. spending multiplier is given by, “dY/dG = 1/0.1 = 10.

=> if dY=9, => dG = (1 – b)*dY = 0.1*9 = 0.9 billion < 1 billion.

=> here govt have to increase spending by “0.9 billion” to accomplish same increase in “Y”.

So, we can see that the increase in “G” is less than the decrease in “T” to increase the same increase in “Y” by “9 billion”. Now, the important question that arises is that, what is the reason behind this situation?

So, we will get our answer if we look at the value of the multiplier, if we talk about “tax multiplier”, which is equal to “-9 < 0”, => if “T” decrease in by “1 billion”, => “Y” will increase by “9 billion”. Similarly, if we talk about “govt. spending multiplier”, which is equal to “10 > 0”, => if “G” decrease in by “1 billion”, => “Y” will increase by “10 billion”, => dY under “G” is more because of the multiplier, the “G” multiplier is more in absolute term. So, given this if we want the same increase in “Y” then absolutely the increase in “G” must be less than decrease in “T”.